Neile's parabola

Also known as the semi-cubical parabola,
a curve discovered by the English mathematician William Neile (1637–1670)
in 1657. It was the first algebraic
curve to have its arc length calculated.
(Before this, only the arc lengths of transcendental curves such as the
cycloid and the logarithmic
spiral had been calculated.)

Christiaan Huygens showed that this curve
satisfies the requirement asked for in 1687 by Gottfried Leibniz,
namely, the curve along which a particle may descend under gravity
so that it moves equal vertical distances in equal times. Neile's parabola
is the evolute of a parabola.